“Geometry of Numbers” in a context of algebraic theory of numbers

2016

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DOI 10.3103/s1066369x16100133
Data confidence 70 medium
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Abstract

As noted in circumstantial monograph “Geometry of Numbers” by P. M. Gruber and C. G. Lekkerkerker, lately there is no considerable contribution to classical theory of calculation and estimates of critical determinants. In this paper, in a certain sense, we fill a gap in a retardation occurred in developing of this theme. We propose a new theoretical-numerical approach with numerous consequences which, in fact, allows to revise all these subjects from another position.